Moments of Compound Renewal Sums with Dependent Risks Using Mixing Exponential Models

Fouad Marri, Franck Adekambi and Khouzeima Moutanabbir
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Fouad Marri: Department of Statistics and Actuarial Science, Institut National de Statistique et d’Economie Appliquée, INSEA, Rabat 10112, Morocco
Khouzeima Moutanabbir: Department of Mathematics and Actuarial Science, The American University in Cairo, New Cairo 11835, Egypt

Risks, 2018, vol. 6, issue 3, 1-17

Abstract: In this paper, we study the discounted renewal aggregate claims with a full dependence structure. Based on a mixing exponential model, the dependence among the inter-claim times, the claim sizes, as well as the dependence between the inter-claim times and the claim sizes are included. The main contribution of this paper is the derivation of the closed-form expressions for the higher moments of the discounted aggregate renewal claims. Then, explicit expressions of these moments are provided for specific copulas families and some numerical illustrations are given to analyze the impact of dependency on the moments of the discounted aggregate amount of claims.

Keywords: renewal process; discounted aggregate claims; copulas; archimedean copulas (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:6:y:2018:i:3:p:86-:d:165708

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